Our correspondent says that part of the problem is the extraordinary vagueness of the EU-brokered ceasefire deal, which speaks only of "additional security measures" in "the immediate proximity of South Ossetia" - proximity being defined as a distance of "several kilometres".
While Georgia insists that Russian troops must leave its territory, a senior Russian general said the situation remained unstable, accusing Georgia of planning further military operations.
Following a statement by the Russian defence ministy that the withdrawal was complete, US President George W Bush and his French counterpart, Nicolas Sarkozy, expressed their disatisfaction.
They agreed in a telephone call that "Russia is not in compliance" with the ceasefire pact and it should comply immediately, US officials said.
No more use of force
Stop all military actions for good
Free access to humanitarian aid
Georgian troops return to their places of permanent deployment
Russian troops to return to pre-conflict positions
International talks about security in South Ossetia and Abkhazia
"[The Russians] have without a doubt failed to live up to their obligations. Establishing checkpoints, buffer zones are definitely not part of the agreement," the White House said.
Earlier, the deputy chief of the Russian General Staff, Gen Anatoly Nogovitsyn, said that nearly 2,600 "peacekeeping" troops with armoured cars and helicopters would remain inside Georgia for the foreseeable future.
Gen Nogovitsyn said Russian troops were setting up checkpoints on the borders of South Ossetia and Abkhazia with Georgia.
But the so-called "zone of responsibility" also includes Georgia's main airbase at Senaki, some 40km (25 miles) from the boundary with Abkhazia, which sits astride vital road and rail links to the Black Sea port of Poti.
BBC correspondents on the ground say they have seen what appears to be a significant Russian troop movement out of Georgia.
The BBC's Gabriel Gatehouse in Igoeti - just 35km (21 miles) from the capital, Tbilisi - says he saw Russian troops leave the town, joining a column of hundreds of armoured vehicles on the road towards South Ossetia.
Our correspondent says buses of Georgian police are arriving in Igoeti to take control after Russian troops removed their roadblocks and pulled out.
But another correspondent in the nearby town of Korvaleti says Georgian police vehicles there are still being blocked at checkpoints.
Russia's four-day war with Georgia began after Tbilisi tried to retake the Moscow-backed breakaway province of South Ossetia on 7 August, following days of clashes with separatists.
Thousands of civilians are reported to be in urgent need of relief supplies
The fighting ended with an EU-brokered ceasefire deal, and a promise by Moscow to pull back the bulk of its forces by 22 August.
The commander of US forces in Europe, Gen John Craddock, said earlier that Russia was taking too long to withdraw, and added "if they are moving, it is at a snail's pace".
Meanwhile, the United Nations High Commissioner for Refugees, Antonio Guterres, who has been visiting South Ossetia, said he was deeply moved by the humanitarian problem there and called for the early voluntary return of all refugees.
The UN estimates that nearly 160,000 people have been displaced across the whole of Georgia since the conflict began.
The Georgian government is seeking $1-2bn (£0.5-1bn) in aid to repair and develop infrastructure following the conflict with Russia, the head of the US government aid agency, USAid, said.
The World Bank has also announced that it is sending a team of experts to the country to assess its reconstruction needs.
'War with Nato'
Diplomatic efforts at the UN have reached deadlock over rival resolutions on the crisis from France and Russia.
Russia has reiterated its opposition to a rival French text, which reaffirms Georgia's territorial integrity.
FROM THE TODAY PROGRAMME
Georgia's President Mikhail Saakashvili told the BBC he would never accept what he called Russia's "annexation of its territory".
He warned that Russia's involvement in South Ossetia, Abkhazia and Georgia was intended to send a strong message to the West, and he called for "a united response" from Nato.
"It's all about reconsidering the role of Nato, the role of international law and borders in this part of the world. This is no longer about Georgia anymore," he said.
"Russia decided to win war with Nato without firing a single shot at it."
A Nato spokeswoman says Russia's defence ministry has decided to halt all military co-operation with the bloc to protest at what Moscow calls the alliance's biased, pro-Georgian view of the conflict.
The move by Moscow followed a Nato statement that there would be no "business as usual" with Moscow unless its troops pulled out of Georgia.
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